Quasinormal modes of black holes in scalar-tensor theories with nonminimal derivative couplings

We study the quasinormal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The spacetime differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasinormal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and nonminimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found in general relativity.